Intermediately subcritical branching process in random environment: the initial stage of the evolution

TL;DR

This paper studies the early evolution of an intermediately subcritical branching process in a random environment, focusing on its behavior conditioned on long-term survival.

Contribution

It provides new insights into the initial stage dynamics of such processes, which was previously not well understood.

Findings

Characterization of the process's behavior during the initial stage

Conditions under which the process survives for a long time

Mathematical description of the process's evolution in the initial phase

Abstract

We consider branching process evolving in i.i.d. random environment. It is assumed that the process is intermediately subcritical. We investigate the initial stage of the evolution of the process given its survival for a long time.